How do we use computational models of cognitive processes?

Previously I outlined a scheme for understanding the usefulness of computational models.1 This scheme was accompanied by two specific proposals. Firstly, that although models have diverse purposes, the purposes of individual modelling efforts should be made explicit. Secondly, that the best use of modelling is in establishing the correspondence between model elements and empirical objects in the form of certain 'explanatory' relationships: prediction, testing, existence proofs and proofs of sufficiency and insufficiency. The current work concerns itself with empirical tests of these two claims. I survey highly cited modelling papers and from an analysis of this corpus conclude that although a diverse range of purposes are represented, neither being accompanied by an explicit statement of purpose nor being a model of my 'explanatory' type are necessary for a modelling paper to become highly cited. Neither are these factors associated with higher rates of citation. The results are situated within a philosophy of science and it is concluded that computational modelling in the cognitive sciences does not consist of a simple Popperian prediction-and-falsification dynamic. Although there may be common principles underlying model construction, they are not captured by this scheme and it is difficult to imagine how they could be captured by any simple formula.